Interaction between Ethereal Absolution versus Edgar Markov with Captivating Vampire
The vampire tokens will enter as 1/1 creatures and remain on the battlefield.
Both the -1/-1 effect from Ethereal Absolution and the +1/+1 effect from Captivating Vampire are continuous effects, generated by their respective static ability. These effects do not grant counters, and the abilities are not triggered. They are simply true, and immediately affect any object they do affect; there is no delay. Objects that are affected enter the battlefield with the modifications already active.
Continuous effects are handled in layers. Power/Toughness-changing effects happen in layer 7:


Interaction of Continuous Effects

613.1g Layer 7: Power- and/or toughness-changing effects are applied.

Within layer 7, there are sublayers for the different kinds of P/T-changing effects:

613.3. Within layer 7, apply effects in a series of sublayers in the order described below. Within each sublayer, apply effects in timestamp order. (See rule 613.6.) Note that dependency may alter the order in which effects are applied within a sublayer. (See rule 613.7.)
613.3c Layer 7c: Effects that modify power and/or toughness (but don’t set power and/or toughness to a specific number or value) are applied.

Both the +1/+1 and the -1/-1 are in that layer.
Within a layer or sublayer, the effects are applied in timestamp order, i.e. generally the order in which the abilities that generated the effects started working. However, in this case it doesn't matter, the +1/+1 and -1/-1 just cancel each other out, no matter which is applied first.