Self-supervised Vision Transformers (ViTs) like DINO show an emergent ability to discover objects, typically observed in [CLS] token attention maps of the final layer. However, these maps often contain spurious activations resulting in poor localization of objects. This is because the [CLS] token, trained on an image-level objective, summarizes the entire image instead of focusing on objects. This aggregation dilutes the object-centric information existing in the local, patch-level interactions. We analyze this by computing inter-patch similarity using patch-level attention components (query, key, and value) across all layers. We find that: (1) Object-centric properties are encoded in the similarity maps derived from all three components ($q, k, v$), unlike prior work that uses only key features or the [CLS] token. (2) This object-centric information is distributed across the network, not just confined to the final layer. Based on these insights, we introduce Object-DINO, a training-free method that extracts this distributed object-centric information. Object-DINO clusters attention heads across all layers based on the similarities of their patches and automatically identifies the object-centric cluster corresponding to all objects. We demonstrate Object-DINO's effectiveness on two applications: enhancing unsupervised object discovery (+3.6 to +12.4 CorLoc gains) and mitigating object hallucination in Multimodal Large Language Models by providing visual grounding. Our results demonstrate that using this distributed object-centric information improves downstream tasks without additional training.