Isolated published scientific studies report it's possible although difficult to graft pawpaws. But you probably won't see any mention of this propagation technique in your usual reference sources because of several important characteristics of the species.

•	Almost exclusively, growers from backyarders to big commercial operations worldwide use seed propagation because each fruit produces hundreds of viable seeds that store well, germinate easily and can produce fruit in less than a year with ideal climatic conditions and optimal management.
•	It is one of the very few major fruit tree crops in the world propagated in this way, as usually there's a more prolonged juvenile period over some years with seedlings, and vegetative propagation usually halves this non-productive period.
•	The superior fruiting qualities of selected cultivars, normally desired in other fruits which require vegetative or micro-propagation techniques to be maintained, are less important in pawpaws. The hermaphrodites favoured in tropical climates can become almost pure breeding lines after several generations of controlled in-breeding as they primarily self-pollinate. In sub-tropical climates like ours, the dioecious varieties perform better, and although subject to normal sexual variation can be manageable with selection of seed from superior trees and by restricting open pollination from unknown males or hermaphrodites. At least half the gene pool in this situation (the female side) has been selected.
•	Pawpaws have very strong apical dominance which results in them normally being single-trunked, with axial fruiting occurring as meristematic buds located in the tip region differentiate into flowers. As an herbaceous, soft-wooded and hollow-stemmed species, this region is very delicate and not hardened to minimise desiccation as in other more woody species. Lateral buds lower down the stem remain inhibited under normal conditions, but can develop slowly following injury or pruning of the apical region. This means scion material for grafting is typically non-ideal, either too delicate from the tip and requiring fastidious control of humidity, or strongly inhibited if lower segments are used.
•	Normal grafting (eg whip or cleft) requires matching of the cambial regions of scion and rootstocks, but unless relatively mature males are used for the rootstock there'll be a gross mismatch in diameters between them.
•	The species is lactiferous, which interferes with timely union of cambial regions from scion and rootstock.

A principal problem that all growers face with seedling propagation is that it's not possible to determine sex in the field before flowering. As a consequence the common practice is to put 3-4 seedlings in the one planting hole, wait till flowering then cull those males or non-vigorous females not needed. With dioecious varieties only one male is needed to pollinate several females and this means considerable time and resources have been wasted raising these superfluous plants. For the home grower who is only interested in a small number of plants, Murphy's Law inevitably kicks in and the several potted plants you've grown up ready for in-ground planting could be almost all males. Like everyone else I've been propagating my plants by seeds and I replace my chosen 3-4 mature females every few years to keep up yield and quality, so I always have new plants coming through. In the past I've just killed the unwanted excess males and hoped the females would give good quality fruit, but it's still a bit hit and miss.

This year for the first time I decided to have a go at a graft - the unwanted male would have been sacrificed anyway and if it didn't take there'd be nothing lost. One of my females was in the last year of production and I'd topped it to reduce height. The expected lower branching slowly developed, providing smaller diameter scion material in vegetative growth mode. Then, a decision had to be made on which way to go, the tip region or lower down the branch? I decided to go with the latter and hoped I could get the graft to take with sufficient lateral bud growth before it all dried out. This meant it was far easier to match diameters of scion and rootstock for a cleft graft as the small male seedling had just started to produce flowers. So far it looks like it's going to work, as shown in the picture. If so, I'm assured of getting fruit the equivalent of my best quality tree and it could become the main way I generate stock for each renewal cycle. There's a further favourable possibility – males are usually more vigorous than females so a grafted plant on male rootstock could also be more vigorous, giving greater yield. A tip if you decide to have a go – the very soft stem material provides little mechanical strength to hold the scion firmly, so bind tightly with grafting tape and keep the scion relatively short so it won't be too top heavy.

Update

Literature reports indicate cleft grafting can be successful with pawpaws, and consequently this was the first technique I tried. However the very soft-wooded lateral branches that are the most likely source of suitably responsive dormant buds mean that without external support, the slowly desiccating scion can wilt and become difficult to maintain in firm and fixed cambial contact with the rootstock in the period before the union becomes functional. I thought a side graft could effectively address this limitation as the remaining root stock above the graft area would provide a ready-made stabilising ‘post’ for anchoring the scion. A further consideration was that root stock leaves left above the graft would ensure continuation of sap flow around the graft region and enhance the chances of take. Result - within two weeks I had new growth in the scion, and this rapidly went on to the level shown in the picture. It seems to be a better way to go than top working with a cleft graft.

Pawpaw side graft update 2

This picture taken several months later shows the plant growing on nicely after not doing very much over an unusually long, cold winter and spring this year. Already forming flower buds and hopefully good fruit will come through in the not-too-distant future, given the female scion pedigree.

Pawpaw side graft update 3

Fruit set in autumn, stalled through winter and is now maturing nicely. This illustrates such vegetative propagation gives fairly rapid fruit production of selected phenotype. Graft region can be seen at about knee height.