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<div class="parent">
<p class="child">天地左右の中央に配置</p>
</div>

.parent {
  position: relative;
}
.child {
  position: absolute;
  top: 50%;
  left: 50%;
  -webkit-transform: translate(-50%, -50%); /* Safari用 */
  transform: translate(-50%, -50%);
}