Partial staking means that a stakee sells pieces of between 1% and 99% of his staking offer at a predetermined rate. Some players might charge a markup. The involved parties also agree on a percentage that specifies the cut.
Another type of partial staking is a situation for example, where the stakee invests money himself (for example in a cash game staking). In this case, both parties provide a part of the bankroll and the stakee carries a residual risk. Again, the involved parties agree on a cut at the beginning of the staking.